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NK-Labeling of GraphsDOI: 10.4236/ajcm.2024.144020, PP. 391-400 Keywords: Graph, Edge Coloring, NK-Labeling, Label, Path, Cycle, Wheel, Complete Graph Abstract: A graph labeling is the assigning of labels to the vertices, edges, or both (usually non-negative integers), often satisfying some prescribed requirements. This terminology has become standard. A graph G's edges can be colored by assigning a different color to each of its edges. The edge coloring is appropriate if adjacent edges are given different colors. In this work, we introduce a new labeling called NK-labeling. Let be a proper edge coloring of G which induces a proper vertex coloring defined by Such that is the set of edges incident with in G. The minimum positive integer for which the graph G has NK-labeling called NK-chromatic index and denoted by . We study the NK-labeling of several well-known classes of graphs. It is shown that the NK-chromatic of the path for is three and for odd
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